KIEV, Ukraine (AP) — An exit poll on Sunday showed that billionaire candy-maker Petro Poroshenko won Ukraine’s presidential election outright in the first round — a vote that authorities hoped would unify the deeply fractured nation.

Long lines snaked around polling stations in Kiev for the vote but heavily armed pro-Russia rebels in eastern Ukraine intimidated locals by smashing ballot boxes, shutting down polling centers and issuing threats.

Sunday’s ballot took place despite weeks of fighting in the sprawling eastern regions that form Ukraine’s industrial heartland, where pro-Russia separatist have seized government buildings and battled government troops. The rebels had vowed to block the ballot in the east — and less than 20 percent of the polling stations were open there.

The exit poll for Sunday’s election, conducted by three respected Ukrainian survey agencies, found the 48-year-old candy tycoon Poroshenko getting 55.9 percent of the vote.

In a distant second was former prime minister Yulia Tymoshenko with 12.9 percent, the poll showed. Full results are expected to be announced Monday in the election that could be a critical step toward resolving Ukraine’s crisis.

Oligarch businessman Vadim Rabinovich, the head of the Ukrainian Jewish Parliament, polled well beneath Tymoshenko.

The poll, which surveyed 17,000 voters at 400 precincts, claimed a margin of error of 2 percentage points, indicating Poroshenko clearly passed the 50-percent mark needed to win without a runoff. It was conducted by the Razumkov Center, Kiev International Sociology Institute and the Democratic Initiatives Foundation.

The election came three months after the country’s pro-Russia leader fled in February, chased from power by months of protests over corruption and his decision to reject a pact with the European Union and forge closer ties with Moscow, and two months after Russia annexed Crimea.

Yet the question of who was able to vote Sunday loomed large over the democratic process. Some 35.5 million Ukrainians were eligible to vote, but separatists in the eastern Donetsk and Luhansk regions — which have 5.1 million voters — said they will not hold the vote because they are no longer part of Ukraine.

Little voting was taking place in the east. The regional administration in Donetsk said only 426 of 2,430 polling stations in the region were open Sunday, and none in the city of Donetsk, which has 1 million people. There was no voting in the city of Luhansk either, but some stations were open in the wider Luhansk region.

Fighting broke out Sunday in the Luhansk town of Novoaidar, where an AP reporter heard heavy gunfire. Areas north of the town, 50 kilometers (30 miles) north of the rebel-held city of Luhansk, are under the control of pro-government forces.

Sergei Melnichuk, a Ukrainian army battalion commander stationed in Novoaidar, said about 50 armed pro-Russia rebels attacked a polling station trying to seize ballots already cast. He said they were thwarted and 13 of them were captured.

The Interfax-Ukraine news agency quoted deputy interior minister as saying one person was killed and another injured in the fighting.

Poroshenko decried the deadly clashes in his country after casting his ballot Sunday in Kiev, where many people wore traditional embroidered shirts in a sign of Ukrainian patriotism.

Russian President Vladimir Putin has promised to “respect the choice of the Ukrainian people” and said he would work with the winner, in an apparent bid to ease Russia’s worst crisis with the West since the Cold War and avoid a new round of Western sanctions.

Many voters appreciate Poroshenko’s pragmatism and his apparent knack for compromise, a unique trait in a political environment long dominated by intransigent figures. Poroshenko strongly backs closer ties with the 28-nation EU, but also speaks about the need to normalize ties with Russia.

“He is a very smart man who can work hard compared to others, and he is also a businessman and knows that compromises are necessary even if unpleasant,” said 55-year old Kiev teacher Larisa Kirichenko. She also voiced hope that Poroshenko will negotiate a peaceful solution to the problems in the east.

The interim Kiev government and the West have accused Russia of backing the separatist uprising. Moscow has denied the accusations but annexed Ukraine’s Black Sea peninsula of Crimea after a separatist vote there.

Ukraine and the rest of the world have not accepted Moscow’s annexation of Crimea, so residents there who wanted to vote Sunday were allowed to travel to other areas in Ukraine. It was not clear how many did so.

Ukrainian election officials said they have received as little as 26 percent of the election registers for the Donetsk region and 16 percent for the Luhansk region. Ukraine’s deputy interior minister, Serhiy Yarovyi, said police could only ensure security at polling stations in just nine of the 34 electoral districts in the east.

There were plenty of disruptions Sunday in Donetsk. A convoy of an armored personnel carrier and seven trucks carrying several hundred heavily armed men drove through central Donetsk. The gunmen got out of the trucks, stood to attention and shot into the air in jubilation as several thousand supporters cheered them.

A team of insurgents visited polling stations Sunday in Donetsk to make sure they were closed. At one station, Vyacheslav Kucher, 36, tested the front door and gave a thumbs-up sign after finding it locked.

“I am checking to see everything is normal, to see that there is no nonsense, so this junta doesn’t come to power,” Kucher said.

Outside the Donetsk administration building, which has been occupied by rebels since early April, a group of masked men drove up carrying confiscated ballot boxes and made a show of smashing them in front of news cameras.

One polling station in Donetsk opened but minutes later gunmen arrived and forced its election commission out. Gunmen also stormed the Donetsk village council in Artemivka that was hosting a polling station and set it ablaze, the Ukrainian Interior Ministry said.

Yet some parts of the Donetsk region remain under greater government control so voting could take place.

In the Azov Sea port of Mariupol, 202 out of the city’s 216 polling stations were working. Just over a week ago, Rinat Akhmetov, the billionaire metals tycoon who is Ukraine’s richest man, had workers from his factories in Mariupol join police to patrol the city and evict the pro-Russia insurgents from government buildings.

“I want order in this country. We can’t continue without a president. We need order,” voter Gennadiy Menshykov said in Mariupol.

In the town of Krasnoarmeisk, in the western Donetsk region, a trickle of people came to cast their ballots.

Ivan Sukhostatov, 37, said he had voted for peace.

“We came to show that this whole situation is contrived,” he said. “One side are called terrorists, the others get called fascists. But we have no differences between us. We have one faith, we speak one language. We just want there to be peace.”